Philosophy 109, Modern Logic, Queens College Russell Marcus, Instructor email: philosophy@thatmarcusfamily.org website: http://philosophy.thatmarcusfamily.org Office phone: (718) 997-5287

Introduction, §§1.1 and 1.4

I. Defining ‘Logic’ Consider the following pair of definitions: A. Logic is the study of argument. B. Arguments ares what logic studies. There is a circularity here, which makes the definitions unhelpful. This circularity is a formal result. We study formal results, in logic.

Now, replace B., above, with: B’. An argument is a set of statements, called premises, intended to establish a specific point, called the conclusion. This is a better definition, not circular, and reduces terms to simpler ones.

An alternative description of logic: the rules of reasoning. A big philosophical question: Is logic descriptive, representing how we actually reason? Or is it prescriptive, setting out rules for good reasoning? Before we can start to answer this question, we have to see what logic looks like, at least a bit.

Here’s another definition: a ‘proposition’, or a ‘statement’, is a declarative sentence that has a truth value. We will consider only two truth values: true and false. There are logics with more. The most interesting have three, or infinitely many. Here, we’ll mostly keep it simple, at first.

II. Separating Premises from Conclusions

Our first task is to analyze arguments, indicating their structures, separating premises from conclusions.

Consider the following argument: ‘We may conclude that eating meat is wrong. This may be inferred from the fact that we must kill to get meat. And killing is wrong.’

The conclusion is: ‘Eating meat is wrong.’ The premises are: ‘We must kill to get meat. Killing is wrong.’ Note the elimination of certain words: these are indicators.

Here are some conclusion indicators: therefore, we may conclude that, we may infer that, entails that, hence, thus, consequently, so, it follows that, implies that, as a result...

Here are some premise indicators: since, because, for, in that, may be inferred from, given that, seeing that, for the reason that, inasmuch as, owing to... ‘and’ often indicates the presence of an additional premise.

When formally representing arguments, we omit indicators. We (partially) formally represent the argument in the following manner: P1: We must kill to get meat. P2: Killing is wrong. C: Eating meat is wrong.

A few guidelines and tips: The order of the premises is unimportant. The number of premises is unimportant: you may combine or separate premises, at times. Sometimes, a sentence may contain both a premise and a conclusion, and so must be divided. Natural language is inexact, and non-formulaic. Note that not all sentences will contain indicators. You will have to judge from the content of the propositions which are premises and which are conclusions. The best way to determine premises and conclusions is to determine what the main point is, and then look to see what supports that point. Many arguments contain irrelevant, extraneous information. Many arguments contain implicit information; these are called ‘enthymemes’.

III. Exercises A. Represent the following arguments in premise/conclusion form.

1. The psychological impact and crisis created by the birth of a defective infant is devastating. Not only is the mother denied the normal tension release from the stress of pregnancy, but both parents feel a crushing blow to their dignity , self- esteem, and self-confidence. In a very short time, they feel grief for the loss of the normal, expected child, anger at fate, numbness, disgust, waves of helplessness and disbelief.

2. Neither a borrower nor a lender be, For loan oft loses both itself and friend, And borrowing dulls the edge of husbandry.

3. If a piece of information is not "job relevant," then the employer is not entitled qua employer to know it. Consequently, since sexual practices, political beliefs, associational activities, etc., are not part of the descriptions of most jobs, that is, since they do not directly affect one's job performance, they are not legitimate information for an employer to know in the determination of the hiring of a job applicant.

IV. Validity and Soundness

Consider the following three arguments. Are they good? 1) All persons are mortal. Socrates is a person. ˆ Socrates is mortal.

This is a good argument.

2) All men are fish. Joe is a man. ˆ Joe is a fish.

The conclusion follows from the premises, but the premises are false.

3) All Toyotas are cars. I own a car. ˆ I own a Toyota.

The conclusion doesn’t follow from the premises.

Note that the last two are bad for different reasons: 3) is invalid, 2) is valid, but unsound.

The validity of an argument depends on its form. An argument is valid if the conclusion follows logically from the premises. Certain forms are valid. Certain forms are invalid The soundness of a avalid argument depends on truth of its premises. A valid argument is sound if its premises are true. Only valid arguments can be sound.

The most important sentence of this course: In deductive logic, if the form of an argument is valid and the premises are all true, then the conclusion must be true.

In invalid arguments, the premises can be true at the same time that the conclusion is false, though all can be true. Validity is independent of truth. Validity is related to possibility, while soundness is related to truth.

V. Exercises B. Are the following valid? If so, are they sound?

1. If it snows more than a foot, Queens College will be closed. It snowed more than a foot last Monday. Therefore, Queens College was closed.

2. The Mets are a professional baseball team. Professional baseball teams are sports businesses. So, the Mets are a sports business.

3. If police departments improve their effectiveness, crime rates go down. Crime rates have gone down. So, police departments have improved their effectiveness.

4. Since the sun is pink, and made of cheese, it follows that some cheese is pink.

5. Some cars are green. Some cars are Toyotas. So, some cars are green Toyotas.

6. All great singers have strong voices. Celine Dion does not have a strong voice. So Celine Dion is not a great singer.

VI. Solutions Answers to Exercise A. 1. Premise 1: Not only is the mother denied the normal tension release from the stress of pregnancy, but both parents feel a crushing blow to their dignity , self-esteem, and self-confidence. Premise 2: In a very short time, they feel grief for the loss of the normal, expected child, anger at fate, numbness, disgust, waves of helplessness and disbelief. Conclusion The psychological impact and crisis created by the birth of a defective infant is devastating.

2. Premise 1: Loan oft loses both itself and friend. Premise 2: Borrowing dulls the edge of husbandry. Conclusion: Neither a borrower nor a lender be.

3. Premise 1: If a piece of information is not "job relevant," then the employer is not entitled qua employer to know it. Premise 2: Sexual practices, political beliefs, associational activities, etc., are not part of the descriptions of most jobs, that is, they do not directly affect one's job performance, Conclusion: They are not legitimate information for an employer to know in the determination of the hiring of a job applicant.

Answers to Exercise B: 1. Valid, unsound 2. Valid, sound 3. Iinvalid 4. Valid, unsound 5. Invalid 6. Valid, unsound